Cain Lebihan, 21, lashed out in violence in the Hill View area on Wednesday, July 20.
He committed the offences while subject to a suspended prison term – and has now been warned that it may be activated when he is sentenced in August.
Magistrates in South Tyneside heard Lebihan had turned up at a first sister’s home, in Thorney Close, to ask for help but in breach of a restraining order.
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He left after 10 minutes when she refused to let him in and threatened to call police, but he ventured only as far as his mother’s address.
Prosecutor Glenda Beck said he banged on his parent’s door and left but returned at around 11pm.
Mr Beck said: “He banged on the door, asking for help. She refused to let him in.
“He refused to go but then turned down the path and she followed. He turned and said, ‘Come on then, come on then’.
“She slipped and fell. He then ripped out a gatepost and raised it above his head. He then punched his other sister in the face.
“He came back moments later with a hammer and threw it at the house but missed.
“He left the address, and the police were called, but he came back and caused damage to a marked police vehicle by smashing the windscreen.”
In a victim statement, Lebihan’s mum said she was worried he would return and damage her home.
Lebihan pleaded guilty to charges of assault by beating against the sister, common assault against his mother, breaching a restraining order and causing £300 of criminal damage to the police car.
He also admitted a charge of causing £2,000 of criminal damage to his mum’s Mercedes car and her gatepost.
And he also pleaded guilty to a public order charge of provoking fear of violence.
The offences put Lebihan in breach of a suspended prison sentence, imposed at Newcastle Crown Court in November, for charges of criminal damage and breaching a restraining order.
Joanne Gatens, defending, said: “Cain has spiralled, probably since turning 18 and he appears before the court on a regular basis from around the time of his 17th birthday.
“His relationship with his parents broke down and he’s been in and out of prison since then.
“More recently, he’s been sleeping on a building site, avoiding workmen, because he had nowhere else to go.
“He went to the houses to ask for help and for somewhere to stay. That doesn’t excuse his behaviour.
“I feel desperately sorry for this young man. He’s 21 and his life has spiralled.
“I’ve conceded, and Cain would concede, that custody today is inevitable if you sentence.”
Magistrates remanded Lebihan into custody and sent him to be sentenced at Newcastle Crown Court on Tuesday, August 23.